A wide variety of systems for computerized authentication of documents are known.
According to Wikipedia, the Phong reflection model, developed in 1973, is an empirical model of the local illumination of points on a surface. Phong's methods have become “the de facto baseline shading method for many rendering applications.”
Applications: According to Wikipedia, the Phong reflection model is used “to shade surfaces in 3D computer graphics software (and) to model the reflection of thermal radiation from the Pioneer probes”.
The Phong reflection model provides an equation for computing the illumination of each surface point Ip:
      I    p    =                    k        a            ⁢              i        a              +                  ∑                  m          ∈          lights                    ⁢                        (                                                                      k                  d                                ⁡                                  (                                                                                    L                        ^                                            m                                        ·                                          N                      ^                                                        )                                            ⁢                              i                                  m                  ,                  d                                                      +                                                                                k                    s                                    ⁡                                      (                                                                                            R                          ^                                                m                                            ·                                              V                        ^                                                              )                                                  α                            ⁢                              i                                  m                  ,                  s                                                              )                .            Where:                ks, is a specular reflection constant, the ratio of reflection of the specular term of incoming light,        kd, is a diffuse reflection constant, the ratio of reflection of the diffuse term of incoming light (Lambertian reflectance),        kα, is an ambient reflection constant, the ratio of reflection of the ambient term present in all points in the scene rendered,        α, is a shininess constant for this material, which is larger for surfaces that are smoother and mirror-like. When this constant is large, the specular highlight is small.        {circumflex over (L)}m, is the direction vector from the point on the surface toward each light source (m specifies the light source),        {circumflex over (N)}, is the normal at this point on the surface,        {circumflex over (R)}m, is the direction that a perfectly reflected ray of light would take from this point on the surface, and        {circumflex over (V)}, is the direction pointing towards the viewer (such as a virtual camera).where direction vector {circumflex over (R)}m is computed as the reflection of {circumflex over (L)}m on the surface characterized by the normal {circumflex over (N)} to the surface using:{circumflex over (R)}m=2({circumflex over (L)}·{circumflex over (N)}){circumflex over (N)}−{circumflex over (L)}m         
The disclosures of all publications and patent documents mentioned in the specification, and of the publications and patent documents cited therein directly or indirectly, are hereby incorporated by reference. Materiality of such publications and patent documents to patentability is not conceded.